What is this?
A Lissajous curve is the path traced when two perpendicular harmonic motions combine. The frequency ratio between the horizontal and vertical axes (a/b) determines how many lobes and crossings the figure has. A phase offset δ shifts where the path opens and closes, turning a diagonal line into a circle, or a simple loop into a figure-eight.
Notes
The canvas plots x = sin(a · t + δ) and y = sin(b · t). Phase δ, which is just when the difference in time when the curves start, advances automatically over time, so the same ratio morphs continuously as the horizontal axis leads or lags the vertical one.
At 1:1, the curve passes through a circle when δ reaches 90°; at 1:2, it passes through a vertical figure-eight. Lissajous curves show up in logos too, Meta’s mark can be seen at a 1:2 ratio.